We present a new integral representation for the flux of the advection-diffusion-reaction equation, which is based on the solution of a local boundary value problem for the entire equation, including the source term. The flux therefore consists of two parts, corresponding to the homogeneous and particular solution of the boundary value problem. Applying Gauss-Legendre quadrature rules to the integral representation gives the high order finite volume complete flux scheme, which is fourth order accurate for both diffusion dominated and advection dominated flow.
|Title of host publication||Numerical Analysis and Applied Mathematics (Proceedings ICNAAM 2009, Rethymno, Crete, Greece, September 18-22, 2009)|
|Editors||T.E. Simos, G. Psihoyios, C. Tsitouras|
|Place of Publication||Melville NY|
|Publisher||American Institute of Physics|
|Publication status||Published - 2009|
|Name||AIP Conference Proceedings|
Anthonissen, M. J. H., & Thije Boonkkamp, ten, J. H. M. (2009). A compact high order finite volume scheme for advection-diffusion-reaction equations. In T. E. Simos, G. Psihoyios, & C. Tsitouras (Eds.), Numerical Analysis and Applied Mathematics (Proceedings ICNAAM 2009, Rethymno, Crete, Greece, September 18-22, 2009) (pp. 410-414). (AIP Conference Proceedings; Vol. 1168). Melville NY: American Institute of Physics. https://doi.org/10.1063/1.3241484